Determination of the Bessel light beam cone parameter by Fourier analysis of the diametral distribution of the intensity

Abstract

Power spectral density (PSD) of the intensity distribution of an ideal Bessel light beam (BLB) expressions are obtained. It is shown that the PSD of the intensity distribution of an ideal BLB is limited and the upper boundary of the PSD is equal to the doubled cone parameter (the product of the wave number and the sine of the half angle of the cone of wave vectors), and the number of zeros in the PSD of an ideal BLB located in the interval from zero frequency to the upper boundary of the spectrum, is equal to the order of the beam. A technique is proposed for estimating the cone parameter of BLBs by analysing the PSD estimates of diametral distributions – one-dimensional intensity distributions obtained in the transverse plane of the beam along a line passing through the beam axis from transverse two-dimensional BLB intensity distributions recorded in the form of digital computer images. The influence of clipping (the end of the distribution at the boundary of the sensitive sensor), Gaussian and cosine modulations of the diametral distribution on the shape of the spectrum and, in case of clipping, the error in the cone parameter estimation using the proposed method is investigated. The technique is tested on the example of the analysis of experimental BLBs of different orders (BLBm, m = 0, 1, 2). The proposed technique can be used to assess the quality parameters of the BLB. The results of the analysis of the influence of cosine modulation on the shape of the PSD can be used to assess the magnitude of the rounding of the apex of the axicon forming the BLB for control the quality of the axicon manufacturing.